Equivalent Circuit Element Calculation of Gapped Multiwinding Inductors

Abstract

Accurate and fast models of the equivalent circuit (EC) elements of gapped multiwinding inductors are essential for the design of galvanically isolated converters, such as Flyback and LLC converters. Typically, the EC elements are acquired from measurements or time-consuming FEM simulations, both of which are disadvantageous for optimizing the design of the magnetic device. This paper proposes a multiwinding magnetic device EC that exclusively uses the impedance matrix elements, i.e., self- and mutual impedances. The advantage of the impedance matrix equivalent circuit (IMEC) is that self- and mutual impedances are directly measurable. Furthermore, the paper presents an analytical 2D magnetic field model to calculate the EC elements. It is quantitatively confirmed that frequency significantly affects the resistances and the inductances of magnetically coupled windings. In particular, eddy currents in windings induced by the fringing field of the air gap play a role besides the well known skin and proximity effect. The proposed model accurately considers all these effects in foil, Litz, and round wire conductors. The model is verified using FEM simulations and measurements.